\documentclass[11pt]{article}

\begin{document}

\declare{syntax={infix,5,"+",l}, meaning=arith1.sum}
$1+(2+3)$
\begin{theorem}
\declare{syntax={infix,7,"*",l}, meaning=arith1.times}
$5+4$
$5*4$
$1+(2*(3+4)+5)*6+7*8$
\begin{lemma}
\declare{syntax={infix,7,"/",l}, meaning=arith1.divide}
$$1/2$$
$(a+8)/6*17$
\end{lemma}
\end{theorem}
$$(34+(8+6))$$
\end{document}